# Team-Specific Hitter Values by Markov

In my first article, I wrote about the limitations of the linear weights system that wOBA is based on when it comes to the context of unusual team offenses. In my second, I explained how Tom Tango, wOBA’s creator, also came up with a way of addressing some of these limitations by deriving a new set of linear weights for different run environments, thanks to BaseRuns. Today, I will tell you about the next step in the evolution of run estimators — the Markov model. Tom Tango created such a model that can be accessed through his website, and I’ve turned that model into a spreadsheet that I’ll share with you here.

I’ve told you that the problem with the standard run estimator formulas is that they make assumptions about what a hit is going to be worth, run-wise, based on what it was worth to an average team. That means it’s not going to apply very well to an unusual team. What’s so great about the Markov is that it makes no such assumptions — it figures all of that out itself, specific to each team. And when I say it figures it out, I mean it basically calculates out a typical game for that team, given the proportion of singles, walks, home runs, etc. the team gets in its plate appearances. It therefore estimates the run-scoring of typical teams better than just about anything, but it also theoretically should apply much, much better to very unusual or even made-up teams.

### Will this spreadsheet thing make my life complete?

Well, not really. But it is fun to explore. The thing I think it’s most useful for is to guess how many runs a team would score with or without certain players. To demonstrate why this may be eye-opening for you, I’m going to show you how even two players with identical wOBA and wRC+ ratings could have significantly different offensive values to different teams.

### Markov: I must break you…r perceptions of player values

In 2011, Mark Trumbo and Alberto Callaspo had identical wOBAs (0.328) and therefore identical wRC+ as well (108), seeing as how they both played for the Angels. However, they achieved these above-average wOBAs in very different ways: Callaspo with a 0.366 OBP and 0.375 SLG, and Trumbo with a 0.291 OBP and 0.477 SLG. So, let’s place these two onto various teams to see what happens. To keep things simple, let’s just pretend there’s no such thing as park effects.

Now, before I get into this, let me remind you that teams don’t have a fixed number of plate appearances per season, but their number of outs in a season is close to fixed; e.g. 162 games/season * 9 innings/game * 3 outs/inning = 4374 outs. Of course, it’s not exactly that, mainly because of extra innings and the fact that the home team won’t have a full 9 innings of offense in games they win. Anyway, I’m going to try to equalize Trumbo and Callaspo for playing time by giving them the same number of outs, defined as: Outs = PA – H – BB – HBP + CS + GDP. Ideally, that would also add outs on the bases as well, but FanGraphs doesn’t provide that as of yet.

Another thing: I really ought to be removing a player from each of these teams to make room for Trumbo or Callaspo, but so as not to add the additional variable of different players being removed from different teams, we’ll just reduce each team’s outs (and the rest of their numbers proportionally) to make room. This means we’re basically just pretending that all the original players on that team had their playing time reduced a bit to make room.

So, without further ado, here’s what happens when 2011 Trumbo’s (T) or Callaspo’s (C) numbers are inserted into various especially good or bad offenses:

Season Team or Player OBP SLG Aggro Actual Markov (tweaked) Markov (default) BaseRuns Runs Created
2011 Mark Trumbo 0.291 0.477 -0.193 ? 4.440 4.765 4.828 5.066
2011 Alberto Callaspo 0.366 0.375 -0.043 ? 4.988 5.211 5.125 5.219
1963 Colt .45’s 0.283 0.301 0.190 2.864 2.837 2.774 2.921 2.959
1963 Colt .45’s+T 0.284 0.318 0.154 ? 2.997 2.975 3.115 3.156
1963 Colt .45’s+C 0.292 0.308 0.165 ? 3.023 2.978 3.114 3.162
1965 Mets 0.277 0.327 0.119 3.018 2.956 2.968 3.121 3.153
1965 Mets+T 0.278 0.342 0.089 ? 3.187 3.144 3.289 3.327
1965 Mets+C 0.286 0.332 0.105 ? 3.215 3.145 3.292 3.343
1968 Mets 0.281 0.315 0.238 2.902 2.945 2.850 3.035 3.110
1968 Mets+T 0.282 0.331 0.199 ? 3.094 3.040 3.214 3.289
1968 Mets+C 0.290 0.321 0.208 ? 3.120 3.042 3.216 3.300
2011 Mariners 0.292 0.348 0.195 3.432 3.454 3.385 3.538 3.608
2011 Mariners+T 0.292 0.361 0.159 ? 3.554 3.525 3.670 3.749
2011 Mariners+C 0.300 0.351 0.171 ? 3.590 3.537 3.681 3.763
1994 Yankees 0.374 0.462 -0.283 5.929 5.904 6.516 6.404 6.630
1994 Yankees+T 0.364 0.464 -0.271 ? 5.663 6.227 6.163 6.427
1994 Yankees+C 0.373 0.450 -0.246 ? 5.774 6.331 6.223 6.423
1996 Mariners 0.366 0.484 -0.197 6.168 6.098 6.526 6.452 6.765
1996 Mariners+T 0.360 0.483 -0.196 ? 5.911 6.328 6.279 6.602
1996 Mariners+C 0.366 0.473 -0.178 ? 5.989 6.397 6.323 6.607
1999 Indians 0.373 0.467 -0.161 6.228 6.119 6.547 6.454 6.688
1999 Indians+T 0.366 0.468 -0.162 ? 5.925 6.340 6.279 6.538
1999 Indians+C 0.373 0.457 -0.148 ? 6.006 6.414 6.321 6.535

A bit more explanation: besides the default version of the Markov that Tango has on his site, as well as the simple versions of BaseRuns and Bill James’ Runs Created that the webpage also produces, I’ve listed the results for a slightly altered version of the Markov that I came up with, which attempts to account for certain factors that are missing from the Markov (I’ll talk more about this later). The “aggro” factor is my stab at measuring base running aggression and effectiveness that I use in the tweaked Markov.

So, at the top two spots on the list, we have the theoretical runs scored of teams full of clones of either Trumbo or Callaspo. This is basically the same idea as the RC27 you can find amongst ESPN.com’s sabermetric stats (which places Trumbo at 4.47 and Callaspo at 5.22, by the way). You can see right away that the Markovs favor Callaspo over Trumbo more than you might expect from their wOBAs and wRC+. Do you remember seeing the exponential growth curve of runs depending on team OBP in my last article? That explains why this is the case — it’s an important team effect that wOBA doesn’t try to account for.

You’ll also notice that relative to Trumbo, Callaspo is worth a lot more to the good offenses than to the bad ones. In particular he’s worth more to the high-OBP teams, as besides the exponential impact his better OBP has on runs, his relative lack of power hurts less. That’s because the value of a single to a high-OBP team is greater than it is to a low-OBP team, especially relative to a HR (see the graphs in my second article if that confuses you). There is a threshold of team suckitude at which 2011 Trumbo’s offense would become more valuable to a team than 2011 Callaspo’s, but it appears that even a bad team in the deadball era of the 60s is still a little bit short of that.

### Play along at home or work

I took a page out of Bradley Woodrum’s book and I’m giving you a peek via the Excel Web App. Just click on the green Excel icon in the bottom right area of the app to download the spreadsheet (about 1 MB in size). Once you’ve downloaded it, you’ll be able to paste data from the Standard section of team batting numbers from FanGraphs (link) into the “Enter Data Here” tab of my spreadsheet, or enter whatever you want manually. You’ll then be able to see the results of the calculations on the “Results” tab (surprise), which you should be able to find near the bottom of the spreadsheet. Here ya go:

### The Perfect Run Modeler? Almost.

Tom Tango says his model is “mathematically perfect,” but readily acknowledges that it’s a bit simplistic, ignoring not only steals (SB) and caught stealing (CS), but grounded into double plays (GIDP) and other outs on bases (OOB). To properly account for these factors would require a much more complicated model, but I’ve come up with some modifications that attempt to account for those factors, without fundamentally changing Tango’s model.

The first thing I did was to reduce each team’s expected plate appearances per game by their expected GIDP and CS per game, along with an empirically-derived OOB constant tied to their on base rates. It’s not a perfect solution, because, for one, OOB rates aren’t so constant, as James Gentile recently pointed out at THT. You can, however, get OOB data from Baseball-Reference.com, if you have the patience and the desire. Another issue (I think) is that GIDP rates are dependent on how likely it is for a batter to have men on base, which would mean, for example, that I shouldn’t be penalizing a team full of 9 Trumbos so much for GIDP, because that team would be less likely to be able to hit into one. That could be worked out better, but it’s tricky.

The other main thing I did was to create the aforementioned base running aggressiveness modifier to the extra-base-taking rates that are essential to the model (they’re really the main assumptions in the model that are a bit tricky to estimate). It’s based on things like steals and caught stealing per runner on 1B, as well as 3B/2B. It’s probably not so proper that I’ve also included GIDP/PA as a major factor here, but the last trick I did didn’t fully account for the negative impact of GIDPs. I also included team OBP and SLG as factors, as one can expect weaker teams to be more aggressive on the base paths due to low odds of scoring without taking extra bases.

Finally, I changed the default extra-base-taking rates to be more in-line with Tango’s empirical findings. Of course, those rates aren’t entirely stable. Feel free to change anything in the “Results” tab that is bordered in red, as you see fit. You can even mess around with the “Calculations” tab if you know your stuff.

Well, that’s my time. Hope you’ve enjoyed. There’s plenty more I can say about this subject, if you’re interested — let me hear your questions and comments, and if you’d like to see me apply this to something else or make changes.

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Steve is a robot created for the purpose of writing about baseball statistics. One day, he may become self-aware, and...attempt to make money or something?

Guest
sprained left fat
3 years 6 months ago

can’t wait to download this sheet when I get home (have to do work now). this looks like great stuff – thanks!

Guest
dafuq
3 years 6 months ago

Excellent.

Guest
LaLoosh
3 years 6 months ago

good freakin lord.

Member
Roto Wizard
3 years 6 months ago

I heart this. I also feel this is why people hate advanced statistics. It’s difficult for most people to support something they can barely read, let alone understand.

Guest
LaLoosh
3 years 6 months ago

I generally support most advanced metrics, but what’s the possible application of this particular one? I’m not saying there isn’t one but’s it’s not readily apparent. If the answer is that there doesn’t have to be one and it’s just a “fun theoretical exercise,” well then yeah it’s a venture into the uber-esoterica.

Member
Member
philosofool
3 years 6 months ago

For a team that has decide who 7 or 8 of it’s everyday hitters are with an estimate of the run environment that they create, it could be a good way to figure out which FA are most worthwhile to pursue.

Guest
Baltar
3 years 6 months ago

… and evaluate prospective trades. I’d like to think that there are smart teams (Rays?) already doing something like this.

Guest
dafuq
3 years 6 months ago

That is the most ignorant comment I’ve possibly ever read. Who would ever want an accurate run estimator!!

Guest
LaLoosh
3 years 6 months ago

“the most ignorant….”

jeez, what an imbecile.

Guest
telly
3 years 6 months ago

He asked a legitimate question. Don’t be a dick, just politely answer it.

Guest
grady
3 years 6 months ago

Oh my god.

Member
Spit Ball
3 years 6 months ago

Digging deep for the answers, I like it. Could you now add in the park effects please. (jus KIDDIN) Great work Steve!

Guest
AverageMeansAverageOverTime
3 years 6 months ago

I will be busy for weeks with this stuff. Thanks.

Guest
Chummy Z
3 years 6 months ago

I have nothing smart to say to this. Just wow.

Member
Member
philosofool
3 years 6 months ago

Nice work. Confirms the rule of thumb that the value of slugging goes up as OBP decreases while the value of OBP goes up as slugging increases. I always say that the handy way to think about it is this:
Imagine a team that draws a walk 95% of the time. They will scored dozens of runs in a game and a home run won’t add much.
Imagine a team that gets out 95% of the time. A player that reaches base will almost never score. Home runs are nearly the only way to score.

Guest
Baltar
3 years 6 months ago

This is basically what Steve showed in his previous article.

Guest
LaLoosh
3 years 6 months ago

I know this is going to infuriate the thinnest skinned sabres in the community, but isn’t this sort of instinctual on its own? I mean don’t we already look at a team and say that guys like Mark Trumbo need players in front of him like Callaspo to get on base so that his XBH ability can be maximized?

Isn’t there (in theory) already some thought process that goes into constructing a lineup with the idea of maximizing run creation? Obviously not all managers look at this the same way, but I’m just saying that no one looks at each player without considering his affect on the rest of the lineup.

Guest
browl
3 years 6 months ago

Doesn’t this article claim that Trumbo would be relatively more valuable on a bad OBP team?

This actually runs counter to instinct. A team with a good leadoff hitter would actually be better served by adding another leadoff hitter.

Member
Nevin
3 years 6 months ago

Hot.

Guest
Baltar
3 years 6 months ago

You are already one of my favorite FanGraphs authors. Keep it up!

Member
kdm628496
3 years 6 months ago

could you use this at the start of the offseason to determine the “best fit” for free agents?

Guest
wiggly
3 years 6 months ago

Sorry to be clueless, but I’m pretty unsure of what to make of this. For the first part, it seems like the upshot is that maybe wOBA’s weights are a little off such that OBP is a little undervalued vis a vis SLG. Then it looks like you do a lot of stuff and show that in the end, you kind of get back where you started: wRC+/ wOBA gets transformed, but in the end when you look at Runs Created (last column) after the magic, it turns out that in most cases the teams get very nearly the same improvement from two players with identical wOBAs even if the wOBAs are achieved differently. If the author or another commenter could clarify a little more I’d appreciate it. Thanks.

Guest
wow
3 years 6 months ago

beautiful.

Guest
3 years 6 months ago

I think the only step up from this is a good Monte Carlo or Simulator. With a Monte Carlo you are able to get a sense of how lineup construction mixes in with skillsets (high/low OBP, high/low SLG). Kind of like this.

Member
3 years 6 months ago

Great! Thank you so much for the article and the spreadsheet.

Guest
Bill
3 years 6 months ago

I think that this could also be used as a developmental tool, not just something to help evaluate FAs. Specifically, since most smaller market teams depend on player devolopment and home grown talent, this could be used to develop a consistent philosophy.

What I’m getting outside of the compounding effect that OBP and slugging have when surrounded by “like” talent, is that it might be less beneficial to construct a diverse lineup. But I don’t have the savvy to properly look into that.

Guest
3 years 6 months ago

This looks very neat.

I never went anywhere with it, but Mike Hunnersen and I used to talk about narrowing the context for batters in an offence to the 3 or 4 batters around them, with the idea that someone batting 2nd doesn’t have so much influence over the person batting 7th, and the other way around. We would probably use this kind of idea, but perhaps limit the context to half the batting order, to at least arrive at a good estimate not only of a player’s impact on the overall offence, but roughly speaking which groups of batters should hit together in the lineup, which could aid in lineup construction, or at the least lead to strange insights like “if X is forced into the lineup, put Y in there, too”.

(Of course, you might believe that batting order is totally unimportant. I think it matters, but it’s nowhere near the bottleneck in tweaking team offensive performance, so I’d attack bigger questions first.)

Guest
TomC
3 years 6 months ago

Something’s bothering me here. wOBA comes from linear weights, and linear weights come from modern offense, so in theory, the offense provided by two players with the same wOBA should be equally valuable to an average modern offense, and nearly equally valuable to anything close to an average modern offense, but what you’ve done shows Callaspo anywhere from beating to clobbering Trumbo over the entire range of modern offenses. That can’t be right (unless wOBA is way wrong).

I think there’s a problem in the way you handled the outs. Holding team outs constant is fine, but you can’t multiply by 8/9 and then add 1/9 Callaspo or 1/9 Trumbo outs in because they don’t make outs at close to the same rate (which is the whole point). By allocating Callaspo the same number of outs as Trumbo, you’re effectively adding in a lot more Callaspo PAs than Trumbo PAs, and since he’s an above average hitter, that improves offenses. I think you need to figure out how many outs each is expected to make on a team with 8/9 original out% and 1/9 new player out% (Callaspo less than 1/9th, trumbo more than 1/9th of team outs) and then add in their stats based on that number of outs.